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Alexy Vincenzo's user avatar
Alexy Vincenzo's user avatar
Alexy Vincenzo's user avatar
Alexy Vincenzo
  • Member for 11 years, 11 months
  • Last seen more than 2 years ago
7 votes

Suppose $f$ and $g$ are entire functions, and $|f(z)| \leq |g(z)|$ for all $z \in \mathbb{C}$, Prove that $f(z)=cg(z)$.

6 votes

Let $f$ be a holomorphic in $D(0,1)$, with Re$\,f(z) >0$ and $f(0)=1.$ Then $\lvert\, f'(0)\rvert\leq 2$

3 votes

Let $p,q$ be odd primes such that $p-q=4a.$ Prove that $\Bigg(\dfrac{a}{p}\Bigg)=\Bigg(\dfrac{a}{q}\Bigg).$

2 votes

Show: $\max_{|z|=R} \operatorname{Re}\left(z\frac{f'(z)}{f(z)}\right) \geq N $

2 votes

$f \in {\mathscr R[a,b]} \implies f $ has infinitely many points of continuity.

1 vote

In a UFD, lcm = product for coprimes: $\,(a,b)=1,\ a,b\mid c\Rightarrow ab\mid c$

1 vote

If $f$ is an odd function that is holomorphic in $\mathbb{C}- \{0\}$ such that $|f(z)| \leq \frac1{|z|}+ |z|^2$, then $f(z) = \frac{a_{-1}}{z} + a_1z$

1 vote

All conformal maps from $\mathbb{H} $ to $\mathbb{D}$ are of the form $\frac{e^{i\theta}(z-\beta)}{z-\overline{\beta}}$

0 votes

Help needed to understand proof to Darboux Sum Comparison Lemma

0 votes

A secant inequality for convex functions

0 votes

Fitzpatrick's proof of Darboux sum comparison lemma

0 votes

Does there exists an entire function with the following property: $f\left(\frac{1}{n}\right)= \frac{n^4}{1+n^4}, n =1,2,...$

0 votes

If $p \equiv 3 \ (\text{mod} \ 4)$ is a prime, show $(\frac{p-1}{2})! \equiv (-1)^{t} \ (\text{mod} \ p)$